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Multi-Echelon Inventory – June 15, 2006 Stochastic Multi-Echelon Systems Need to set y at each stage Could use base-stock formula  But how to quantify lead time?  Lead time is stochastic  Depends on upstream base-stock level and stochastic demand For serial systems, exact algorithms exist  Clark-Scarf (1960)  But they are cumbersome

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Multi-Echelon Inventory – June 15, 2006 An Approximate Method Assume that each stage carries sufficient inventory to deliver product within S periods “most of the time”  Definition of “most” depends on service level constant, z   S is called the committed service time (CST) We simply ignore the times that the stage does not meet its CST  For the purposes of the optimization  Allows us to pretend LT is deterministic

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Multi-Echelon Inventory – June 15, 2006 Net Lead Time Each stage has a processing time T and a CST S Net lead time at stage i = S i+1 + T i – S i 321 T3T3 T2T2 T1T1 S3S3 S2S2 S1S1 “bad” LT“good” LT

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Multi-Echelon Inventory – June 15, 2006 Decentralized Systems So far, we have assumed the system is centralized  Can optimize at all stages globally  One stage may incur higher costs to benefit the system as a whole What if each stage acts independently to minimize its own cost / maximize its own profit?

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Multi-Echelon Inventory – June 15, 2006 Contracting One solution is for the parties to impose a contracting mechanism  Splits the costs / profits / risks / rewards  Still allows each party to act in its own best interest  If structured correctly, system achieves optimal cost / profit, even with parties acting selfishly There is a large body of literature on contracting  In practice, idea is commonly used  Actual OR models rarely implemented

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Multi-Echelon Inventory – June 15, 2006 Irrational Behavior Causes BWE Firms over-react to demand signals  Order too much when they perceive an upward demand trend  Then back off when they accumulate too much inventory Firms under-weight the supply line Both are irrational behaviors Demonstrated by “beer game”